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  • The classical concept of affine locally symmetric spaces allows a generalization for various geometric structures on a smooth manifold. We remind the notion of symmetry for parabolic geometries and we summarize the known facts for |1|-graded parabolic geometries and for almost Grassmannian structures, in particular. As an application of two general constructions with parabolic geometries, we present an example of non-flat Grassmannian symmetric space. Next we observe there is a distinguished torsion-free affine connection preserving the Grassmannian structure so that, with respect to this connection, the Grassmannian symmetric space is an affine symmetric space in the classical sense.
  • The classical concept of affine locally symmetric spaces allows a generalization for various geometric structures on a smooth manifold. We remind the notion of symmetry for parabolic geometries and we summarize the known facts for |1|-graded parabolic geometries and for almost Grassmannian structures, in particular. As an application of two general constructions with parabolic geometries, we present an example of non-flat Grassmannian symmetric space. Next we observe there is a distinguished torsion-free affine connection preserving the Grassmannian structure so that, with respect to this connection, the Grassmannian symmetric space is an affine symmetric space in the classical sense. (en)
Title
  • Remarks on Grassmannian symmetric spaces
  • Remarks on Grassmannian symmetric spaces (en)
skos:prefLabel
  • Remarks on Grassmannian symmetric spaces
  • Remarks on Grassmannian symmetric spaces (en)
skos:notation
  • RIV/00216224:14410/08:00025215!RIV10-GA0-14410___
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  • P(GP201/06/P379), P(LC505)
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  • 5
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  • 392279
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  • RIV/00216224:14410/08:00025215
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  • parabolic geometries; Weyl structures; almost Grassmannian structures; symmetric spaces (en)
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  • CZ - Česká republika
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  • [4F75D07DBCCA]
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  • Archivum Mathematicum
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  • 44
http://linked.open...iv/tvurceVysledku
  • Zalabová, Lenka
  • Žádník, Vojtěch
issn
  • 0044-8753
number of pages
http://localhost/t...ganizacniJednotka
  • 14410
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